Question
For the binary operation ×7 on the set S = {1, 2, 3, 4, 5, 6}, compute 3−1 ×7 4.

Answer

Finding identity element:
Here,
71 = Remainder obtained by dividing 1 × 1 by 7 = 1
74 = Remainder obtained by dividing 3 × 4 by 7 = 5
75 = Remainder obtained by dividing 4 × 5 by 7 = 6
So, the composition table is as follows:
×7 1 2 3 4 5 6
1 1 2 3 4 5 6
2 2 4 6 1 3 5
3 3 6 2 5 1 4
4 4 1 5 2 6 3
5 5 3 1 6 4 2
6 6 5 4 3 2 1
We observe that all the elements of the first row of the composition table are same as the top-most row.
So, the identity element is 1.
Also, 3×5 = 1
So, 3-1 = 5
Now,
3-1×7 4 = 5×7 4 = 6

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free